Electromagnets usually include a number of closely spaced turns of wire or coil that create a magnetic field. The wire turns are wound around a magnetic core made from a ferromagnetic material. The magnetic core concentrates the magnetic flux to make a powerful electromagnet. The magnetic field can be changed by controlling the amount of electric current in the coil. The electromagnet requires a continuous supply of current to maintain the magnetic field. When current flows in the coil magnetic flux density is generated in the core material which can be concentrated in a single direction. Depending on the design of the electromagnet, the magnetic flux density can provide an attractive force (pull force) on a ferromagnetic target. This “pull” force can be used in electromagnetic reluctance actuators.
An electromagnetic reluctance actuator operates on the principle that a magnetic material, when placed in a magnetic field, will experience a mechanical force tending to move the material in a direction parallel to the field to minimize the system energy. At any point on the surface of the material the reluctance force is proportional to the square of the magnetic flux density B2 of the magnetic field experienced at that point, as shown in Equation [1]:
                                                        F              rel                        -                                          f                ma                            ·              A                                =                                                                      B                  2                                ⁢                A                                            2                ⁢                                  μ                  o                                                      =                                          Φ                2                                            2                ⁢                                  μ                  o                                ⁢                A                                                    ,                            [        1        ]            where Frel is reluctance force, fma is surface force density, A is the pole surface area, B is the magnetic flux density, Φ is magnetic flux and μo is vacuum permeability.
A typical design objective for electromagnetic reluctance actuator is to optimize the electromagnet design to delay magnetic field saturation. Magnetic field saturation is a state reached when an increase in an applied external magnetic field cannot increase the magnetization of the core material further, resulting in the total magnetic flux density leveling off. This may result in a force that is too weak for a particular application.